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The School District of Palm Beach County GEOMETRY HONORS 3rd Quarter Scope 2010 - 2011 Benchmarks Topic & Suggested Pacing Next Generation Sunshine State Standards January 4 March 11 MA.912.D.9.3 Use vectors to model and solve application problems. 8.5 Explore and use other sequences found in nature such as the MA.912.D.11.5 Fibonacci sequence and the golden ratio. 7.4 Concept Byte Ratios and Proportions Similar Polygons Proving Triangles Similar Use properties of congruent and similar polygons to solve MA.912.G.2.3 mathematical or real-world problems. 7.1-7.3, 10.4 Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry. Know that images MA.912.G.2.4 formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons. 9.1-9.7 Explain the derivation and apply formulas for perimeter and MA.912.G.2.5 area of polygons (triangles, quadrilaterals, pentagons, etc.). 10.1-10.4 Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations MA.912.G.2.6 in the plane. 9.1-9.3, 9.5 Similarity in Right Triangles The Golden Ratio Proportions in Triangles The Pythagorean Theorem and Its Converse Special Right Triangles Trigonometry Angles of Elevation and Depression Vectors Student Target I can… • Write ratios and solve proportions • Identify and apply similar polygons • Use the AA ~ Postulate and the SAS ~ and SSS ~ Theorems • Use similarity to find indirect measurements • Find and use relationships in similar right triangles • Use the Side-Splitter Theorem and the Triangle-AngleBisector Theorem • Use the Pythagorean Theorem and its converse • To use the properties of 45 – 45 – 90 and 30 – 60 – 90 triangles • Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles • Use angles of elevation and depression to solve problems • Describe vectors • Solve problems involving vector addition • Identify isometries • Find translation images of figures • Find reflection images of figures • Draw and identify rotation images of figures • Identify the type of symmetry in a figure • Understand dilation images of figures • Find compositions of reflections, including glide reflections • Classify isometries • Identify figures that tessellate • Identify transformations and symmetries in tessellations • Find the area of parallelograms and triangles • Find the area of a trapezoid, rhombus, or kite • Find the area of a regular polygon Core Pearson Geometry Honors Gold Series 7.1 7.2 7.3 7.4 7.4 Concept Byte 7.5 8.1 8.2 8.3 8.4 8.5 9.1 9.2 9.3 9.4 9.5 9.6 9.7 10.1 10.2 10.3 10.4 Tutorial Support AYP Support Ratio and Proportion Video MA.912.G.2.3 Similar Shapes Video MA.912.G.2.4 Similar Triangles Video (Part 1) MA.912.G.2.5 Similar Triangles Video (Part 2) MA.912.G.4.6 Pythagorean Theorem Video MA.912.G.5.4 Intro to 30-6090 Triangles Video MA.912.T.2.1 Determine how changes in dimensions affect the perimeter MA.912.G.2.7 and area of common geometric figures. 10.1, 10.3-10.4 Use properties of congruent and similar triangles to solve MA.912.G.4.4 problems involving lengths and areas. 7.1, 7.3, 10.4 MA.912.G.4.5 Apply theorems involving segments divided proportionally. 7.5 Prove that triangles are congruent or similar and use the MA.912.G.4.6 concept of corresponding parts of congruent triangles. 7.3 Use coordinate geometry to prove properties of congruent, Translations Reflections Rotations Symmetry Dilations Compositions of Reflections Tessellations Areas of Parallelograms and Triangles MA.912.G.4.8 regular, and similar triangles. 7.3 MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse. 8.1 Areas of Trapezoids, Rhombuses, and Kites • Find the area of a regular polygon • Find the perimeters and areas of similar polygons 10.4 30 - 60 - 90 Triangles Part II Video 45 - 45 - 90 Triangles Video Basic Trigonometry Video Basic Trigonometry Video II Angles of Elevation and Depression The Basics of Vectors Video Areas of Regular Polygons State and apply the relationships that exist when the altitude MA.912.G.5.2 is drawn to the hypotenuse of a right triangle. Perimeters and 7.4 Areas of Similar Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) MA.912.G.5.3 to solve problems. 8.2, 10.3 MA.912.G.5.4 Solve real-world problems involving right triangles. 7.3, 8.1-8.4 Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them. MA.912.G.6.1 Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons. 10.3 Determine whether a solution is reasonable in the context of MA.912.G.8.3 the original situation. 7.4, 8.1 Translations Figures Reflections Rotations Symmetry Dilations and Similarity Area and Perimeter of Rectangles and Triangles Video Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of MA.912.T.2.1 right triangles. 8.3-8.4 Area of Trapezoids Video Area of Regular Polygons Video Perimeters and Areas of Similar Figures Video Secondary Data-Driven Benchmark Comprehension Check